ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration
We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback–Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly ot...
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| Published in | Applied mathematics and computation Vol. 364; p. 124678 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.01.2020
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| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2019.124678 |
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| Abstract | We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback–Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback–Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality. |
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| AbstractList | We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback–Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback–Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality. |
| ArticleNumber | 124678 |
| Author | Landi, Germana di Serafino, Daniela Viola, Marco |
| Author_xml | – sequence: 1 givenname: Daniela orcidid: 0000-0001-8215-0771 surname: di Serafino fullname: di Serafino, Daniela email: daniela.diserafino@unicampania.it organization: Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, viale A. Lincoln 5, Caserta 81100, Italy – sequence: 2 givenname: Germana surname: Landi fullname: Landi, Germana email: germana.landi@unibo.it organization: Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato 5, Bologna 40126, Italy – sequence: 3 givenname: Marco orcidid: 0000-0002-2140-8094 surname: Viola fullname: Viola, Marco email: marco.viola@uniroma1.it organization: Dipartimento di Ingegneria Informatica, Automatica e Gestionale “Antonio Ruberti”, Sapienza Università di Roma, via Ariosto 25, Roma 00185, Italy |
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| SubjectTerms | Image restoration Iteratively reweighted norm approach Poisson noise Quadratic approximation TV regularization |
| Title | ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration |
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